COVID-19 Outbreak: Worldwide analysis

Quick overview

Current status

#library(nCov2019)
library(leaflet)
library(dplyr)
library(ggplot2)
library(plotly)
library(scales)
library(xts)
library(dygraphs)
library(corrplot)
library(lubridate)
library(fmsb)

COVID<-read.csv("covid_19_data.csv")
COVID_2<-read.csv("COVID19_10-Apr.csv")

Format date:

Date<-as.Date(COVID_2$Date, format="%m/%d/%y") 

COVID_2$Date2<-Date

COVID_updated<-COVID_2 %>% filter(Date2==max(Date2))

leaflet(width = "100%") %>% 
  addProviderTiles("CartoDB.DarkMatter") %>% 
  setView(lng = 0, lat = 10, zoom = 1.5) %>% 
  addCircleMarkers(data = COVID_updated, 
                   lng = ~ Long,
                   lat = ~ Lat,
                   radius = ~ log(Confirmed+1),
                   color = rgb(218/255,65/255,56/255),
                   fillOpacity = ~ ifelse(Confirmed > 0, 1, 0),
                   stroke = FALSE,
                   label = ~ paste(Province.State,",",Country.Region, ": ", Confirmed)
                   )

Current top 10 countries:

COVID_top<-COVID_2 %>% filter(Date2==max(Date2)) %>% 
  group_by(Country.Region) %>% summarise(Total_confirmed=sum(Confirmed)) %>% 
  top_n(10,Total_confirmed) %>% arrange(desc(Total_confirmed))

plot<-ggplot(data=COVID_top
       , aes(x=Total_confirmed,y=reorder(Country.Region,Total_confirmed))) +
  geom_bar(stat ="identity",alpha=0.8,fill="firebrick3") +
  geom_text(aes(label=Total_confirmed), vjust=0.5, hjust=0.9,color="black", size=3.5) +
  scale_x_continuous(labels = comma) +
  labs(title = paste("Top 10 countries with confirmed cases as of ",max(COVID_2$Date2)),
       x = "Confirmed cases",
       y = "Country") +
  theme_minimal()

ggplotly(plot,tooltip = c("x"),width=750)

Time distribution:

COVID_2_Day<- COVID_2 %>% group_by(Date2) %>% summarise(World_confirmed=sum(Confirmed),
                                                        World_deaths=sum(Deaths),
                                                        World_recovered=sum(Recovered))


COVID_Day_confirmed_series<-xts(COVID_2_Day$World_confirmed, order.by=COVID_2_Day$Date2)
COVID_Day_deaths_series<-xts(COVID_2_Day$World_deaths, order.by=COVID_2_Day$Date2)
COVID_Day_recovered_series<-xts(COVID_2_Day$World_recovered, order.by=COVID_2_Day$Date2)

Day_summary<-cbind(COVID_Day_confirmed_series,COVID_Day_deaths_series,COVID_Day_recovered_series)

dygraph(Day_summary, main = "SARS-COV2-outbreak: Total worldwide cases", 
        xlab="Date", ylab="Total cases",width = 750) %>% 
  dySeries("COVID_Day_confirmed_series", "Total cases",drawPoints = TRUE, 
           pointSize = 3, color=rgb(53/255,116/255,199/255)) %>% 
  dySeries("COVID_Day_deaths_series", "Total deaths",drawPoints = TRUE, 
           pointSize = 3, color=rgb(189/255,55/255,48/255)) %>% 
  dySeries("COVID_Day_recovered_series", "Total recovered",drawPoints = TRUE, 
           pointSize = 3, color=rgb(69/255,136/255,51/255)) %>% 
  dyRangeSelector()

New_count<-function(x)
{
  Daily_cases<-numeric(length(x))
  
  for(i in length(x):2)
  {
    Daily_cases[i]=x[i] - x[i-1]
  }
  return(Daily_cases)
}

New_cases<-New_count(COVID_2_Day$World_confirmed)
New_deaths<-New_count(COVID_2_Day$World_deaths)
New_recovered<-New_count(COVID_2_Day$World_recovered)
COVID_New_confirmed_series<-xts(New_cases, order.by=COVID_2_Day$Date2)
COVID_New_deaths_series<-xts(New_deaths, order.by=COVID_2_Day$Date2)
COVID_New_recovered_series<-xts(New_recovered, order.by=COVID_2_Day$Date2)

New_summary<-cbind(COVID_New_confirmed_series,COVID_New_deaths_series,COVID_New_recovered_series)

dygraph(New_summary, main = "SARS-COV2-outbreak: Total worldwide cases", 
        xlab="Date", ylab="Novel coronavirus cases",width = 750) %>% 
  dySeries("COVID_New_confirmed_series", "New cases",drawPoints = TRUE, 
           pointSize = 3, color=rgb(53/255,116/255,199/255)) %>% 
  dySeries("COVID_New_deaths_series", "New deaths",drawPoints = TRUE, 
           pointSize = 3, color=rgb(189/255,55/255,48/255)) %>% 
  dySeries("COVID_New_recovered_series", "New recovered",drawPoints = TRUE, 
           pointSize = 3, color=rgb(69/255,136/255,51/255)) %>% 
  dyRangeSelector()

Team members countries total cases:

COVID_2_Day_Lebanon<- COVID_2 %>% 
  filter(Country.Region %in% c("Lebanon")) %>% 
  group_by(Date2) %>% summarise(World_confirmed=sum(Confirmed))

COVID_2_Day_Chile<- COVID_2 %>% 
  filter(Country.Region %in% c("Chile")) %>% 
  group_by(Date2) %>% summarise(World_confirmed=sum(Confirmed))

COVID_2_Day_Colombia<- COVID_2 %>% 
  filter(Country.Region %in% c("Colombia")) %>% 
  group_by(Date2) %>% summarise(World_confirmed=sum(Confirmed))

COVID_2_Day_CostaRica<- COVID_2 %>% 
  filter(Country.Region %in% c("Costa Rica")) %>% 
  group_by(Date2) %>% summarise(World_confirmed=sum(Confirmed))


COVID_Day_series_Lebanon<-xts(COVID_2_Day_Lebanon$World_confirmed, order.by=COVID_2_Day_Lebanon$Date2)
COVID_Day_series_Chile<-xts(COVID_2_Day_Chile$World_confirmed, order.by=COVID_2_Day_Chile$Date2)
COVID_Day_series_Colombia<-xts(COVID_2_Day_Colombia$World_confirmed, order.by=COVID_2_Day_Colombia$Date2)
COVID_Day_series_CostaRica<-xts(COVID_2_Day_CostaRica$World_confirmed, order.by=COVID_2_Day_CostaRica$Date2)

Our_Countries<-cbind(COVID_Day_series_Lebanon,COVID_Day_series_Chile,COVID_Day_series_Colombia,COVID_Day_series_CostaRica)

dygraph(Our_Countries, main = "SARS-COV2-outbreak: Total cases by country", xlab="Date", ylab="Total cases",width = 750) %>% 
  dySeries("COVID_Day_series_Lebanon", "Lebanon",drawPoints = TRUE, 
           pointSize = 3, color=rgb(0,0,3/255)) %>% 
  dySeries("COVID_Day_series_Chile", "Chile",drawPoints = TRUE, 
           pointSize = 3,color=rgb(120/255,28/255,109/255)) %>% 
  dySeries("COVID_Day_series_Colombia", "Colombia",drawPoints = TRUE, 
           pointSize = 3,color=rgb(237/255,105/255,37/255)) %>% 
  dySeries("COVID_Day_series_CostaRica", "Costa Rica",drawPoints = TRUE,
           pointSize = 3,color=rgb(204/255,197/255,126/255)) %>% 
  dyRangeSelector()

New_Lebanon<-New_count(COVID_2_Day_Lebanon$World_confirmed)
New_Chile<-New_count(COVID_2_Day_Chile$World_confirmed)
New_Colombia<-New_count(COVID_2_Day_Colombia$World_confirmed)
New_CostaRica<-New_count(COVID_2_Day_CostaRica$World_confirmed)

COVID_New_series_Lebanon<-xts(New_Lebanon, order.by=COVID_2_Day_Lebanon$Date2)
COVID_New_series_Chile<-xts(New_Chile, order.by=COVID_2_Day_Chile$Date2)
COVID_New_series_Colombia<-xts(New_Colombia, order.by=COVID_2_Day_Colombia$Date2)
COVID_New_series_CostaRica<-xts(New_CostaRica, order.by=COVID_2_Day_CostaRica$Date2)

Our_New_Countries<-cbind(COVID_New_series_Lebanon,COVID_New_series_Chile,COVID_New_series_Colombia,COVID_New_series_CostaRica)

dygraph(Our_New_Countries, main = "SARS-COV2-outbreak: New cases by country", xlab="Date", ylab="Total cases",width = 750) %>% 
  dySeries("COVID_New_series_Lebanon", "Lebanon",drawPoints = TRUE, 
           pointSize = 3, color=rgb(0,0,3/255)) %>% 
  dySeries("COVID_New_series_Chile", "Chile",drawPoints = TRUE, 
           pointSize = 3,color=rgb(120/255,28/255,109/255)) %>% 
  dySeries("COVID_New_series_Colombia", "Colombia",drawPoints = TRUE, 
           pointSize = 3,color=rgb(237/255,105/255,37/255)) %>% 
  dySeries("COVID_New_series_CostaRica", "Costa Rica",drawPoints = TRUE,
           pointSize = 3,color=rgb(204/255,197/255,126/255)) %>% 
  dyRangeSelector()

Looking for correlations

fig <- plot_ly(COVID_updated, x = ~Confirmed, y = ~Deaths, z = ~Recovered, width=750) %>% 
  add_markers(text= ~Country.Region ,hoverinfo= "text",
              marker = list(color=rgb(189/255,55/255,48/255))) %>% 
  layout(title="Confirmed cases Vs. Deaths Vs. Recovered", scene = list(
                    xaxis = list(title = 'Confirmed'),
                     yaxis = list(title = 'Deaths'),
                     zaxis = list(title = 'Recovered'))) 
fig

For the number of cases

Human Development Index

HDI<-read.csv("Human Development Index (HDI)_2.csv",sep=";",dec=",")

COVID_Country<-COVID_2 %>% filter(Date2==max(Date2)) %>% 
  group_by(Country.Region) %>% summarise(Total_confirmed=sum(Confirmed),
                                         Total_deaths=sum(Deaths),
                                         Total_Recovered=sum(Recovered))

Remove after parentheses:

HDI$Country_2<-gsub("\\s*\\([^\\)]+\\)","",as.character(HDI$Country))

HDI$Country_2[HDI$Country_2=="United States"]<-"US"
HDI$Country_2[HDI$Country_2=="Korea"]<-"South Korea"

Population:

Population<-read.csv("World_population.csv",sep=";",dec=",")

Remove after commma:

Population$Country_Name_2<-gsub(",.*", "", as.character(Population$Country_Name))

Population$Country_Name_2[Population$Country_Name_2=="United States"]<-"US"
Population$Country_Name_2[Population$Country_Code=="KOR"]<-"South Korea"
Population$Country_Name_2[Population$Country_Code=="CZE"]<-"Czechia"

Natural Join:

COVID_3<- COVID_Country %>% inner_join(HDI,by=c("Country.Region"="Country_2")) %>% 
  inner_join(Population,by=c("Country.Region"="Country_Name_2")) %>% 
  select(Country.Region,Total_confirmed,Total_deaths,Total_Recovered,HDI_Rank_2018,Year_2018,
         Country_Code,Population_2018) %>% 
  mutate(Cases_million=(Total_confirmed/Population_2018)*1000000,
         Recovered_percentage=(Total_Recovered/Total_confirmed)*100)  

COVID_3<-COVID_3[!is.na(COVID_3$Population_2018),]

Plot the Human Development Index(HDI) Vs. the number of cases (applying a log transformation), and the proportion of recovered cases:

plot<-ggplot(data=COVID_3,aes(x=log(Cases_million),y=Year_2018,
                        size=Recovered_percentage,text=Country.Region)) +
  geom_point(color="black",fill=rgb(237/255,105/255,37/255),shape=21,alpha=0.6) +
  scale_size(range = c(3,15), name="Recovered \n percentage") +
  theme_minimal() + 
  theme(legend.position="bottom") +
  labs(title="HDI Vs. logarithmus of COVID-19 cases by million inhabitants \n and proportion of recovered",
       x="ln(Cases/1M population)",
       y="HDI")

ggplotly(plot,tooltip = c("text"),width=750)

COVID_numeric_1<-COVID_3 %>% mutate(Log_cases=log(Cases_million),
                                    Death_percentage=(Total_deaths/Total_confirmed)*100) %>% 
  select(Log_cases,Recovered_percentage,Death_percentage,Year_2018)

corrplot(cor(COVID_numeric_1),method = "number",tl.col="black",tl.srt=15,
         col=colorRampPalette(c(rgb(204/255,197/255,126/255),rgb(237/255,105/255,37/255)))(200))

Health expenditure (% of GDP)

Health_expenditure<-read.csv("Health_expenditure_GDP.csv",sep=";",dec=".")

Health_expenditure$Country_2<-gsub("\\s*\\([^\\)]+\\)","",
                                   as.character(Health_expenditure$Country))

Health_expenditure$Country_2[Health_expenditure$Country_2=="United States"]<-"US"
Health_expenditure$Country_2[Health_expenditure$Country_2=="Korea"]<-"South Korea"

COVID_3<- COVID_3 %>% inner_join(Health_expenditure,by=c("Country.Region"="Country_2")) %>% select(-c("Country"))

#write.csv(COVID_3,"COVID_Covariables.csv")

plot<-ggplot(data=COVID_3,aes(x=log(Cases_million),y=Expenditure_2016,
                        size=Recovered_percentage,text=Country.Region)) +
  geom_point(color="black",fill=rgb(204/255,197/255,126/255),shape=21,alpha=0.6) +
  scale_size(range = c(3,15), name="Recovered \n percentage") +
  theme_minimal() + 
  theme(legend.position="bottom") +
  labs(title="Health expenditure (% of GDP) Vs. logarithmus of COVID-19 cases by million inhabitants \n and proportion of recovered",
       x="ln(Cases/1M population)",
       y="% of GDP in health")

ggplotly(plot,tooltip = c("text"),width=750)

Temperature

Temperature<-read.csv("GlobalLandTemperaturesByCountry.csv",sep=";")

Date_Temp<-as.Date(Temperature$dt, format="%d/%m/%Y") 

Temperature$Date_Temp<-Date_Temp

Extract month, filter IQ (Jan, Feb and Mar) and obtain the average IQ temperature:

Temperature<- Temperature %>% mutate(Month=month(Temperature$Date_Temp,label =TRUE),
                                     Year=year(Temperature$Date_Temp)) %>% 
  filter(Month %in% c("Jan","Feb","Mar") & Year>=2000)  %>% 
  group_by(Country) %>% summarise(Avg_IQ_temperature=mean(AverageTemperature))

Temperature<-Temperature[!is.na(Temperature$Avg_IQ_temperature),]

Temperature$Country_2<-gsub("\\s*\\([^\\)]+\\)","",
                                   as.character(Temperature$Country))

Temperature$Country_2[Temperature$Country_2=="United States"]<-"US"
Temperature$Country_2[Temperature$Country_2=="Korea"]<-"South Korea"

COVID_3<- COVID_3 %>% inner_join(Temperature,by=c("Country.Region"="Country_2")) %>% select(-c("Country"))

#write.csv(COVID_3,"COVID_Covariables.csv")

plot<-ggplot(data=COVID_3,aes(x=log(Cases_million),y=Avg_IQ_temperature,
                        size=Recovered_percentage,text=Country.Region)) +
  geom_point(color="black",fill=rgb(120/255,28/255,109/255),shape=21,alpha=0.6) +
  scale_size(range = c(3,15), name="Recovered \n percentage") +
  theme_minimal() + 
  theme(legend.position="bottom") +
  labs(title="Average IQ temperature Vs. logarithmus of COVID-19 cases by million inhabitants \n and proportion of recovered",
       x="ln(Cases/1M population)",
       y="Temperature (Celcius)")

ggplotly(plot,tooltip = c("text"),width=750)

For the number of deaths

###DTP immunization

DTP_immunization<-read.csv("Infants_lacking_immunization_DTP.csv",sep=";")

Remove after parentheses:

DTP_immunization$Country_2<-gsub("\\s*\\([^\\)]+\\)","",
                                 as.character(DTP_immunization$Country))

DTP_immunization$Country_2[DTP_immunization$Country_2=="United States"]<-"US"
DTP_immunization$Country_2[DTP_immunization$Country_2=="Korea"]<-"South Korea"

COVID_4<- COVID_Country %>% inner_join(DTP_immunization,
                                       by=c("Country.Region"="Country_2")) %>% 
  select(Country.Region,Total_confirmed,Total_deaths,Total_Recovered,
         Lack_DTP_inmmunization_2018) %>% 
  mutate(Recovered_percentage=(Total_Recovered/Total_confirmed)*100,
         Death_rate=(Total_deaths/Total_confirmed)*100)

plot<-ggplot(data=COVID_4,aes(x=Death_rate,y=Lack_DTP_inmmunization_2018,
                        size=Recovered_percentage,text=Country.Region)) +
  geom_point(color="black",fill=rgb(204/255,197/255,126/255),shape=21,alpha=0.6) +
  scale_size(range = c(3,15), name="Recovered \n percentage") +
  theme_minimal() + 
  theme(legend.position="bottom") +
  labs(title="% infants lacking DTP immunization Vs. death rate and \n proportion of recovered",
       x="Novel coronavirus death rate",
       y="% of infants")

ggplotly(plot,tooltip = c("text"),width=750)

Infants lacking immunization, measles (% of one-year-olds)

Measles<-read.csv("Measles_immunization.csv",sep=";",dec=".")

Measles$Country_2<-gsub("\\s*\\([^\\)]+\\)","",as.character(Measles$Country))

Measles$Country_2[Measles$Country_2=="United States"]<-"US"
Measles$Country_2[Measles$Country_2=="Korea"]<-"South Korea"

COVID_4<- COVID_4 %>% inner_join(Measles,by=c("Country.Region"="Country_2")) %>% select(-c("Country"))

ggplot(COVID_4, aes(y=Measles_2018)) + 
  geom_boxplot(fill="dodgerblue4",outlier.shape = 21, 
               outlier.fill = "firebrick",alpha=0.75) +
  ggtitle("Boxplot of % infants lacking measles immunization") + ylab("% of infants") +
  theme_minimal()

ggplot(COVID_4, aes(Measles_2018)) + 
  geom_histogram(fill="dodgerblue4",bins=20,alpha=0.8) +
  ggtitle("Histogram of % infants lacking measles immunization") + 
  xlab("% of infants") + 
  ylab("Count") +
  theme_minimal()

plot<-ggplot(data=COVID_4,aes(x=Death_rate,y=Measles_2018,
                        size=Recovered_percentage,text=Country.Region)) +
  geom_point(color="black",fill=rgb(237/255,105/255,37/255),shape=21,alpha=0.6) +
  scale_size(range = c(3,15), name="Recovered \n percentage") +
  theme_minimal() + 
  theme(legend.position="bottom") +
  labs(title="% infants lacking measles immunization Vs. fatality rate \n and proportion of recovered",
       x="Fatality rate (%)",
       y="% of infants")

ggplotly(plot,tooltip = c("text"),width=750)

Fitting a regression model

Transforming with ln and converting temperature as kelvin:

Mod1<-lm(log(COVID_3$Cases_million)~log(COVID_3$Year_2018)+log(COVID_3$Measles_2018)+
           log(COVID_3$Expenditure_2016)+log(COVID_3$Avg_IQ_temperature+273.15))
summary(Mod1)

Call:
lm(formula = log(COVID_3$Cases_million) ~ log(COVID_3$Year_2018) + 
    log(COVID_3$Measles_2018) + log(COVID_3$Expenditure_2016) + 
    log(COVID_3$Avg_IQ_temperature + 273.15))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7927 -0.8026 -0.0988  0.7685  4.6646 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                              28.91233   18.71752   1.545  0.12462    
log(COVID_3$Year_2018)                    8.09219    0.65485  12.357  < 2e-16 ***
log(COVID_3$Measles_2018)                 0.07961    0.11782   0.676  0.50030    
log(COVID_3$Expenditure_2016)             1.00758    0.30867   3.264  0.00137 ** 
log(COVID_3$Avg_IQ_temperature + 273.15) -4.26198    3.29459  -1.294  0.19786    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.36 on 144 degrees of freedom
Multiple R-squared:  0.723, Adjusted R-squared:  0.7153 
F-statistic: 93.96 on 4 and 144 DF,  p-value: < 2.2e-16

Stepwise with AIC critertion:

Mod2<-step(Mod1,direction = "both")

Start:  AIC=88.41
log(COVID_3$Cases_million) ~ log(COVID_3$Year_2018) + log(COVID_3$Measles_2018) + 
    log(COVID_3$Expenditure_2016) + log(COVID_3$Avg_IQ_temperature + 
    273.15)

                                           Df Sum of Sq    RSS     AIC
- log(COVID_3$Measles_2018)                 1     1.326 252.72  87.188
<none>                                                  251.39  88.410
- log(COVID_3$Avg_IQ_temperature + 273.15)  1     3.627 255.02  88.530
- log(COVID_3$Expenditure_2016)             1    19.903 271.29  97.687
- log(COVID_3$Year_2018)                    1   267.232 518.62 193.587

Step:  AIC=87.19
log(COVID_3$Cases_million) ~ log(COVID_3$Year_2018) + log(COVID_3$Expenditure_2016) + 
    log(COVID_3$Avg_IQ_temperature + 273.15)

                                           Df Sum of Sq    RSS     AIC
<none>                                                  252.72  87.188
- log(COVID_3$Avg_IQ_temperature + 273.15)  1     3.451 256.17  87.196
+ log(COVID_3$Measles_2018)                 1     1.326 251.39  88.410
- log(COVID_3$Expenditure_2016)             1    20.945 273.66  96.973
- log(COVID_3$Year_2018)                    1   310.195 562.91 203.715

summary(Mod2)

Call:
lm(formula = log(COVID_3$Cases_million) ~ log(COVID_3$Year_2018) + 
    log(COVID_3$Expenditure_2016) + log(COVID_3$Avg_IQ_temperature + 
    273.15))

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6304 -0.8232 -0.0390  0.8247  4.5290 

Coefficients:
                                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)                               30.1643    18.2214   1.655 0.100014    
log(COVID_3$Year_2018)                     7.6731     0.5772  13.295  < 2e-16 ***
log(COVID_3$Expenditure_2016)              1.0349     0.2996   3.455 0.000724 ***
log(COVID_3$Avg_IQ_temperature + 273.15)  -4.4971     3.2069  -1.402 0.162977    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.325 on 144 degrees of freedom
Multiple R-squared:  0.7221,    Adjusted R-squared:  0.7163 
F-statistic: 124.7 on 3 and 144 DF,  p-value: < 2.2e-16

Normality of residuals:

hist(Mod2$residuals)

shapiro.test(Mod2$residuals)

    Shapiro-Wilk normality test

data:  Mod2$residuals
W = 0.98758, p-value = 0.2094

Prediction power: separate between training and testing:

set.seed(179819)
Sample <- sample(1:length(COVID_3$Cases_million),length(COVID_3$Cases_million)*0.20)
t.testing<- COVID_3[Sample,]
t.training<- COVID_3[-Sample,]

Transform the training and testing variables as before:

t.training<-t.training %>% mutate(Cases_million_log=log(Cases_million),HDI_log=log(Year_2018),
                      GDP_log=log(Expenditure_2016),
                      Temperature_log_kelvin=log(Avg_IQ_temperature+273.15)) 

t.training<-t.training[,14:17]

t.testing<-t.testing %>% mutate(Cases_million_log=log(Cases_million),HDI_log=log(Year_2018),
                      GDP_log=log(Expenditure_2016),
                      Temperature_log_kelvin=log(Avg_IQ_temperature+273.15)) 

t.testing<-t.testing[,14:17]

Fit the same model with training

Mod3<-lm(Cases_million_log~., data=t.training)
summary(Mod3)

Call:
lm(formula = Cases_million_log ~ ., data = t.training)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.4682 -0.7667 -0.0638  0.7399  4.3449 

Coefficients:
                       Estimate Std. Error t value Pr(>|t|)    
(Intercept)             39.0811    18.5629   2.105  0.03744 *  
HDI_log                  7.1009     0.6266  11.332  < 2e-16 ***
GDP_log                  1.0890     0.3331   3.270  0.00142 ** 
Temperature_log_kelvin  -6.1107     3.2665  -1.871  0.06393 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.252 on 115 degrees of freedom
Multiple R-squared:  0.7275,    Adjusted R-squared:  0.7204 
F-statistic: 102.4 on 3 and 115 DF,  p-value: < 2.2e-16

Error functions:

# Residual Sum of Square (RSS)
RSS<-function(Pred,Actual) {
  ss<-sum((Actual-Pred)^2)
  return(ss)
}

# Residual Standard Error (RSE)
RSE<-function(Pred,Real,NumPred) {
  N<-length(Real)-NumPred-1  
  ss<-sqrt((1/N)*RSS(Pred,Real))
  return(ss)
}
# Mean Squared Error 
MSE <- function(Pred,Actual) {
  N<-length(Actual)
  ss<-(1/N)*RSS(Pred,Actual)
  return(ss)
}

# Relative error
RelativeError<-function(Pred,Actual) {
  ss<-sum(abs(Actual-Pred))/sum(abs(Actual))
  return(ss)
}

Prediction:

Pred<-predict(Mod3,t.testing)

Errors:

RSS_Mod3<-RSS(Pred,t.testing$Cases_million_log)
RSE_Mod3<-RSE(Pred,t.testing$Cases_million_log,dim(t.testing)[2]-1)
MSE_Mod3<-MSE(Pred,t.testing$Cases_million_log)
RelativeError_Mod3<-RelativeError(Pred,t.testing$Cases_million_log)

Mod3_Errors<-c(RSS_Mod3,RSE_Mod3,MSE_Mod3,RelativeError_Mod3)

Now, a model without temperature:

t.training <- t.training %>% select(-Temperature_log_kelvin)
t.testing <- t.testing %>% select(-Temperature_log_kelvin)

Mod4<-lm(Cases_million_log~., data=t.training)
summary(Mod4)

Call:
lm(formula = Cases_million_log ~ ., data = t.training)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7017 -0.8447  0.0129  0.7149  4.3942 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   4.3797     0.7074   6.191  9.3e-09 ***
HDI_log       7.6548     0.5582  13.713  < 2e-16 ***
GDP_log       1.2422     0.3263   3.807 0.000227 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.266 on 116 degrees of freedom
Multiple R-squared:  0.7192,    Adjusted R-squared:  0.7144 
F-statistic: 148.6 on 2 and 116 DF,  p-value: < 2.2e-16

Prediction:

Pred<-predict(Mod4,t.testing)

Errors:

RSS_Mod4<-RSS(Pred,t.testing$Cases_million_log)
RSE_Mod4<-RSE(Pred,t.testing$Cases_million_log,dim(t.testing)[2]-1)
MSE_Mod4<-MSE(Pred,t.testing$Cases_million_log)
RelativeError_Mod4<-RelativeError(Pred,t.testing$Cases_million_log)

Mod4_Errors<-c(RSS_Mod4,RSE_Mod4,MSE_Mod4,RelativeError_Mod4)

Create a radarplot:

Errors<-rbind(Mod3_Errors,Mod4_Errors)

rownames(Errors)<-c("Model with temperature","Model without temperature")

colnames(Errors)<-c("Residual Sum of Square","Residual Standard Error","Mean Squared Error","Relative error")

Errors<-as.data.frame(Errors)

maximum<-apply(Errors,2,max)

minimum<-apply(Errors,2,min)

Errors<-rbind(minimum,Errors)

Errors<-rbind(maximum,Errors)

radarchart(Errors,maxmin=TRUE,axistype=4,axislabcol="slategray4",
           centerzero=FALSE,seg=8,cglcol="gray67",
           pcol=c("dodgerblue2","firebrick2","darkorange2","darkorchid2"),
           plty=1,
           plwd=3,
           title="Error comparison")

legenda <-legend(1.5,1, legend=c("With temperature","Without temperature"),
                 seg.len=-1.4,
                 title="Errors",
                 pch=21, 
                 bty="n" ,lwd=3, y.intersp=1, horiz=FALSE,
                 col=c("dodgerblue2","firebrick2","darkorange2","darkorchid2"))